Elliptic curve data - 133560.v4

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  intrinsic_torsion	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '133560bc', 'Clabel': '133560bc3', 'Cnumber': 3, 'abc_quality': 1.0104889048466552, 'absD': 11015708586459788897928023040, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 0, 0, -1143384987, 15714588926374], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 53], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 133560, 'degree': 88178688, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.1328194371184615586252104203', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4], 'jinv': [-221448979693296464284621156, 14756554069224468581115], 'lmfdb_iso': '133560.v', 'lmfdb_label': '133560.v4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -127042776, -582064159680], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '60.12.0-4.c.1.1', '70.6.0.a.1', '84.12.0.?', '120.24.0.?', '140.12.0.?', '168.24.0.?', '280.24.0.?', '420.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 315], [3, 6, 14840], [5, 6, 26712], [7, 8, 19080], [53, 54, 2520]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.0058906423177856217465610340', 'prec': 100}, 'szpiro_ratio': 6.294902555577965, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -4, 0, -6, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, 1, -1, -4, -6, 2, 0, 4, -6, -4, -2, 2, 4, -8, 1, -12, -10, 12, 0, 14, -8, 4, 10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 133560, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '133560.v', 'trace_hash': 2086649778966910834}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.00025720455025904167574295702897', 'prec': 113}, 'conductor': 133560, 'gens': [], 'heights': [], 'lmfdb_label': '133560.v4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.039779074332392810496650872832', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.63646518931828496794641396530743833459', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-39286, 0, 1]], 'xcoord_integral_points': [-39286]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [0, 0], '53': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '133560.v4'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 6055931
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '133560.v4', 'torsion': [4]}
  • id: 6055930
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '133560.v4', 'torsion': [2, 2]}
  • id: 6055932
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '133560.v4', 'torsion': [4]}
  • id: 6055934
    {'degree': 4, 'field': [21, 42, 4, -2, 1], 'lmfdb_label': '133560.v4', 'torsion': [8]}
  • id: 6055933
    {'degree': 4, 'field': [81, 0, 3, 0, 1], 'lmfdb_label': '133560.v4', 'torsion': [2, 4]}
  • id: 6055938
    {'degree': 8, 'field': [-58800, 0, 0, 0, 840, 0, -52, 0, 1], 'lmfdb_label': '133560.v4', 'torsion': [6]}
  • id: 6055937
    {'degree': 8, 'field': [1521, -1638, 2022, -810, 511, -130, 48, -4, 1], 'lmfdb_label': '133560.v4', 'torsion': [2, 8]}
  • id: 6055936
    {'degree': 8, 'field': [9665839225, 0, 0, 0, 334271, 0, 0, 0, 1], 'lmfdb_label': '133560.v4', 'torsion': [8]}
  • id: 6055935
    {'degree': 8, 'field': [2474454841600, 0, 0, 0, -2752820, 0, 0, 0, 1], 'lmfdb_label': '133560.v4', 'torsion': [2, 4]}
  • id: 6055943
    {'degree': 16, 'field': [14656500, 61533000, 97435800, 36529800, -83932980, -128942640, -78718544, -20414768, 1101600, 1850420, 312008, -5832, -2872, 140, 0, -8, 1], 'lmfdb_label': '133560.v4', 'torsion': [12]}
  • id: 6055942
    {'degree': 16, 'field': [6767963469, -18297488280, 17380311072, 1778200992, -749450766, -165518928, 51722244, 2984072, -765493, -7616, 21684, -10456, 1318, 168, -4, -8, 1], 'lmfdb_label': '133560.v4', 'torsion': [2, 6]}
  • id: 6055944
    {'degree': 16, 'field': [140260944825, -130067078400, 77485856400, -19614602928, 6123792756, -421708716, -29592152, 28644520, -5241618, -829672, 77864, -936, 3320, -364, 72, -8, 1], 'lmfdb_label': '133560.v4', 'torsion': [12]}
  • id: 6055941
    {'degree': 16, 'field': [4262635098225, 0, 1240874907300, 0, 48766206300, 0, -768971700, 0, -19309430, 0, -15820, 0, -10020, 0, -100, 0, 1], 'lmfdb_label': '133560.v4', 'torsion': [16]}
  • id: 6055940
    {'degree': 16, 'field': [93483401539860094849, 1407219581317761512, 146364604669450930, -212450115709720, 6490117623435828, 34421862906956, 114832466434, 18615227736, 130869469405, -350047404, 5778206, 8904, 668900, -1484, -28, 0, 1], 'lmfdb_label': '133560.v4', 'torsion': [2, 8]}
  • id: 6055939
    {'degree': 16, 'field': [23917895535735659029636, 0, -1277205911787706312, 0, 212891017496113208, 0, -6766125996924, 0, 782909578325, 0, -2752764, 0, 1376438, 0, 8, 0, 1], 'lmfdb_label': '133560.v4', 'torsion': [4, 4]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 3294219
    {'conductor': 133560, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '133560.v4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3294220
    {'conductor': 133560, 'conductor_valuation': 2, 'discriminant_valuation': 42, 'j_denominator_valuation': 36, 'kodaira_symbol': -40, 'lmfdb_label': '133560.v4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3294221
    {'conductor': 133560, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '133560.v4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3294222
    {'conductor': 133560, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '133560.v4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3294223
    {'conductor': 133560, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '133560.v4', 'prime': 53, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2533117
    {'adelic_gens': [[176, 3, 5, 2], [833, 8, 832, 9], [1, 0, 8, 1], [739, 736, 338, 741], [1, 8, 0, 1], [1, 4, 4, 17], [559, 832, 556, 807], [7, 6, 834, 835], [739, 738, 538, 115], [124, 1, 503, 6]], 'adelic_image': '840.48.0.?', 'conductor': 133560, 'lmfdb_label': '133560.v4', 'prime': 0}
  • id: 518359
    {'conductor': 133560, 'elladic_image': '8.12.0.6', 'lmfdb_label': '133560.v4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 133560.v does not appear in ec_padic